Black holes in full quantum gravity

TL;DR

This work develops a fully quantum, background-independent definition of black holes within loop quantum gravity by identifying the region of a spin network inaccessible to infinity as the black hole. The exterior is described by a single horizon intertwiner living in $H_{\text{horizon}} = Inv[⊗_p H_{j_p}]$, whose dimension $N = \text{dim}(Inv[⊗_p H_{j_p}])$ grows exponentially with horizon area and matches the state space of SU(2) Chern-Simons theory on a punctured surface in the large-$k$ limit. The extra degrees of freedom, encapsulated in the horizon intertwiners, account for black hole entropy and are detectable by exterior measurements via the extrinsic-curvature operator $T_{pp'}$, which encodes horizon-shape information. This framework connects full non-perturbative LQG with CS-based microstate counting, provides a concrete quantum-mechanical picture of horizon microstructure, and offers a bridge to earlier semiclassical treatments and Wheeler's idea of spacetime foam at the Planck scale.

Abstract

Quantum black holes have been studied extensively in quantum gravity and string theory, using various semiclassical or background dependent approaches. We explore the possibility of studying black holes in the full non-perturbative quantum theory, without recurring to semiclassical considerations, and in the context of loop quantum gravity. We propose a definition of a quantum black hole as the collection of the quantum degrees of freedom that do not influence observables at infinity. From this definition, it follows that for an observer at infinity a black hole is described by an SU(2) intertwining operator. The dimension of the Hilbert space of such intertwiners grows exponentially with the horizon area. These considerations shed some light on the physical nature of the microstates contributing to the black hole entropy. In particular, it can be seen that the microstates being counted for the entropy have the interpretation of describing different horizon shapes. The space of black hole microstates described here is related to the one arrived at recently by Engle, Noui and Perez, and sometime ago by Smolin, but obtained here directly within the full quantum theory.